A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

Sensitivity of resolved and parameterized surface drag to changes in resolution and parameterization

The relative contribution of resolved and parameterized surface drag towards balancing the atmospheric angular momentum flux convergence (AMFC), and their sensitivity to horizontal resolution and parameterization, are investigated in an atmospheric model. This sensitivity can be difficult to elucidate in free-running climate models, in which the AMFC varies with changing climatologies and, as a result, the relative contributions of surface terms balancing the AMFC also vary. While the sensitivity question has previously been addressed using short-range forecasts, we demonstrate that a nudging framework is an effective method for constraining the AMFC. The Met Office Unified Model is integrated at three horizontal resolutions ranging from 130 km (N96) to 25 km (N512) while relaxing the model’s wind and temperature fields towards the ERAinterim reanalysis within the altitude regions of maximum AMFC. This method is validated against short range forecasts and good agreement is found. These experiments are then used to assess the fidelity of the exchange between parameterized and resolved orographic torques with changes in horizontal resolution. Although the parameterized orographic torque reduces substantially with increasing horizontal resolution, there is little change in resolved orographic torque over 20N to 50N. The tendencies produced by the nudging routine indicate that the additional drag at lower horizontal resolution is excessive. When parameterized orographic blocking is removed at the coarsest of these resolutions, there is a lack of compensation, and even compensation of the opposite sense, by the boundary layer and resolved torques which is particularly pronounced over 20N to 50N. This study demonstrates that there is strong sensitivity in the behaviour of the resolved and parameterized surface drag over this region

Airborne Measurements of Gravity Wave Breaking at the Tropopause

2000 FLORIDA AVE NW, WASHINGTON, DC, 2000

Impacts of orography on large-scale atmospheric circulation

Some of the largest and most persistent circulation errors in global numerical weather prediction and climate models are attributable to the inadequate representation of the impacts of orography on the atmospheric flow. Existing parametrization approaches attempting to account for unresolved orographic processes, such as turbulent form drag, low-level flow blocking or mountain waves, have been successful to some extent. They capture the basic impacts of the unresolved orography on atmospheric circulation in a qualitatively correct way and have led to significant progress in both numerical weather prediction and climate modelling. These approaches, however, have apparent limitations and inadequacies due to poor observational evidence, insufficient fundamental knowledge and an ambiguous separation between resolved and unresolved orographic scales and between different orographic processes. Numerical weather prediction and climate modelling has advanced to a stage where these inadequacies have become critical and hamper progress by limiting predictive skill on a wide range of spatial and temporal scales. More physically-based approaches are needed to quantify the relative importance of apparently disparate orographic processes and to account for their combined effects in a rational and accurate way in numerical models. We argue that, thanks to recent advances, significant progress can be made by combining theoretical approaches with observations, inverse modelling techniques and high-resolution and idealized numerical simulations

On the critical pair theory in abelian groups : Beyond Chowla's Theorem

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio

Adopting the International Standard 'Becoming a human-centred organization (ISO 27500)' supports a strategic approach to internationalisation.

Educational development is increasingly focussed on quality assurance and enhancement. Individual states/countries have their own mechanisms for assuring the student experience, and this has been accompanied by development of tools (including the UK’s National Student Survey) for capturing student opinion of our efforts. Areas where more work is needed include equity and diversity and it is perhaps time for a fresh approach. In other sectors, International Standards ensure safety, reliability and quality of products and services. Such standards also represent a stakeholder-negotiated (and therefore shared) understanding of ‘good quality’, supporting organisations in accessing new markets and permitting a fair global trade, an approach relevant to higher education. Recent publication of ISO (The International Organization for Standardization) Standard 27500 (the International Standard describing the principles and rationales behind becoming a humancentred organization) seems timely. Encouraging educational institutions to adopt this Standard may offer a strategy for addressing several issues, including internationalisation

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

The Met Office Unified Model Global Atmosphere 7.0/7.1 and JULES Global Land 7.0 configurations

We describe Global Atmosphere 7.0 and GlobalLand 7.0 (GA7.0/GL7.0), the latest science configurations of the Met Office Unified Model (UM) and the Joint UK Land Environment Simulator (JULES) land surface model developed for use across weather and climate timescales. GA7.0 and GL7.0 include incremental developments and targeted improvements that, between them, address four critical errors identified in previous configurations: excessive precipitation biases over India, warm and moist biases in the tropical tropopause layer (TTL), a source of energy non-conservation in the advection scheme and excessive surface radiation biases over the Southern Ocean. They also include two new parametrisations, namely the UK Chemistry and Aerosol(UKCA) GLOMAP-mode (Global Model of Aerosol Processes) aerosol scheme and the JULES multi-layer snow scheme, which improve the fidelity of the simulation and were required for inclusion in the Global Atmosphere/Global Land configurations ahead of the 6th Coupled Model Inter-comparison Project (CMIP6).In addition, we describe the GA7.1 branch configuration, which reduces an overly negative anthropogenic aerosol effective radiative forcing (ERF) in GA7.0 whilst maintaining the quality of simulations of the present-day climate. GA7.1/GL7.0 will form the physical atmosphere/land component in the HadGEM3–GC3.1 and UKESM1 climate model submissions to the CMIP6

Predicting range shifts of African apes under global change scenarios

Aim: Modelling African great ape distribution has until now focused on current or past conditions, while future scenarios remain scarcely explored. Using an ensemble forecasting approach, we predicted changes in taxon-specific distribution under future scenarios of climate, land use and human populations for (1) areas outside protected areas (PAs) only (assuming complete management effectiveness of PAs), (2) the entire study region and (3) interspecies range overlap. Location: Tropical Africa. Methods: We compiled occurrence data (n = 5,203) on African apes from the IUCN A.P.E.S. database and extracted relevant climate-, habitat- and human-related predictors representing current and future (2050) conditions to predict taxon-specific range change under a best- and a worst-case scenario, using ensemble forecasting. Results The predictive performance of the models varied across taxa. Synergistic interactions between predictors are shaping African ape distribution, particularly human-related variables. On average across taxa, a range decline of 50% is expected outside PAs under the best scenario if no dispersal occurs (61% in worst scenario). Otherwise, an 85% range reduction is predicted to occur across study regions (94% worst). However, range gains are predicted outside PAs if dispersal occurs (52% best, 21% worst), with a slight increase in gains expected across study regions (66% best, 24% worst). Moreover, more than half of range losses and gains are predicted to occur outside PAs where interspecific ranges overlap. Main Conclusions: Massive range decline is expected by 2050, but range gain is uncertain as African apes will not be able to occupy these new areas immediately due to their limited dispersal capacity, migration lag and ecological constraints. Given that most future range changes are predicted outside PAs, Africa's current PA network is likely to be insufficient for preserving suitable habitats and maintaining connected ape populations. Thus, conservation planners urgently need to integrate land use planning and climate change mitigation measures at all decision-making levels both in range countries and abroad